Okay, I don't actually do structures and materials so there may be an easier way to do this, but here goes:
I think in this case it may actually be helpful to at least think of the force diagram. There are three forces involved here - the force from the rod, the force from the wire and the weight force of the lamp, and we want the lamp to have a net force of 0. Now, which ways are the forces acting?
Weight force is quite simple, obviously straight down. But the rod is being compressed, so will be exerting a force diagonally upwards on the lamp, while the wire is in tension, so will be exerting a force to the left.
If we resolve these forces, the vertical component of the rod's force must balance out the lamp's weight force, and the horizontal component of the rod's force must balance out the tension in the string.